17 



of u the exposure must be fuur times as lon<», and 

 ia oa sixteea times, because the same light covers 

 respectively four and sixteen times the origmal 

 surface at a. , p ■ 



Let U3 now proceed to lenses, but before coming 

 to a telephotographic lens it will be necessary to 

 know something about the optical properties of 

 its constituent lenses. There are certain elements 

 of a lens necessary to find the magnitude and 

 position of the image. These are the "four 

 Cardinal points," viz., the two focal po,i.(s,and the 

 tmo principal points, but in thin lenses the two 

 latter are usually assumed to coincide in one 

 optical centre. A lens is a portion of a refracting 

 medium bounded by two spherical surfaces of 

 revolution which have a common axis called tne 

 axis of the lens. „ , , t 



I. To determine the centre of the lens. In 

 Pig 2 I with ax as the centre, and ax K the radius, 

 describe the circle R, and with axl as the centre, 

 and ail Rt the radius parallel to the other radius, 

 describe the larger ciicle R, then the piece L is 

 the lens. L < us take this piece out and make it 

 a little larger as Fig. 2 II. Here the line az is the 

 axis of the leQS, let u=i join the two parallel radii 

 by a line meeting the axis of the lens at C, then 

 the point is the centre or optical centre of the' 



ISDS. ^, , . , 



Any riy of light which in passing through the 

 lens passes through C will emerge parallel to its 

 ori.'inal direction or in a very thin lens it wiU 

 practically pass through the lens in a straight line. 



In thick lenses Fig -J. III. there are two prmcx- 

 pal points which do not coincide in one optical 

 centre. Produce the line A to the axis of the lens, 

 and likewise the line D, we then get two new 

 points, Nl N2, which are called the principal or 

 nodal points of the lens. 



These have the property which is evident from 

 the fin-ure that any ray of light proceeding from 

 any direction towards one of these points passes 

 out of the lens as if it had passed through the 



other. ... ,■ 



The centre, to use an Irishism, is sometimes 

 outside the lens altogether, as in Fig 2 IV. Draw 

 the two parallel radii as before, join the ends 

 and produce until the line meets the axis at C, 

 which is the centre of the lens, and the point 

 from which the focal length must be measured 

 not as it is popularly supposed from the middle or 

 the surface of the lens. 



II Todetermine the two focal points of a lens. 

 If a beam ot parallel rays (as rays from the sun 

 or other very distant object) meets one surface of 

 a convex or positive lens in a direction parallel to 

 its axis the rays will, after passing through the 

 lens, meet at a point F, Fig 7 I. This point is 

 called the principal .focus or principal focal 

 point" of the lens and its distance from the 

 centre C of the lens isthe/ocallengtk. Similarly, 

 if we present the second or other surface of the 

 lens to the incident parallel rays they meet again 

 at a point F, which is the second or other focal 

 point. 



No real image can be formed at any position 

 nearer to the centre of (he lens than its principal 

 focus. It is evident that rays from a luminous 

 object placed at its principal focus would, after 

 passing through the lens, emerge parallel, and if 



the object were nearer to C the rays would 

 diverge after passing through the lens. The 

 focal points possess the property that any ray 

 iiicefinj the lens in a direction parallel to the axis 

 of the lens passes through the focal point on the 

 further side of the lens. 



Every lens (or combination ot lenses) may be 

 defined as possessing a centre and two focal points. 

 These elements are sufficient for us to determine 

 the position and magnitude of the image of any 

 object. 



We need not now trouble to draw lenses, but 

 indicate them by the principal plane passing 

 through the centre of the lens, and by setting oft 

 the positions of the focal points on the axis. 



In Pig 3 let L be the lens and C the centre, and 

 A B the object. We have learnt that any ray from 

 A B, parallel to the axis as the line A L, will, after 

 refraction, pass through the focal point F. We 

 have also learnt that any ray passes through the 

 centre without^deviation, as the line A C. The 

 point where these lines meet wUl be the position 

 of the ima^^e of that point of the object. Similarly, 

 we may take any other point of the object as B 

 and draw lines and find the position of the image 

 of that point of the object, and in this way 

 reproduce the object at a b. Xow a step further. 

 The ma.'nitude of the image depends on the 

 distance ot the centre C to the object and the 

 distance of C, to the image. To express these 

 relations we must introduce an optical law known 

 as the -Law of Conjugate Foe". Fig. -^'S really 

 Fig. :i in outline. Suppose the object A B is bO 

 inches away from the centre of the lens, and that 

 the focal length of lens is 10 inches, then the object 

 wUl be 50 inches away from F, or the front focal 

 point ; let us caU this distance x. We shall find 

 that the image a h will be 13 inches fro™ ™«' 

 centre of the lens, or two inches beyond the other 

 principal focus F ; let us call this distance J. 

 Then the focal length of the lens multiplied by 

 itself equals the distance-i multiplied by the 

 distance y, or f,--=xy. The linear size of the 

 image is to that of the object as their respective 

 distances from centre ot lens, or as 12 to 60, that 

 is as one to five, or the magnification is one-htth. 

 A simple method of finding magnification is to 

 divide focal length of lens into i-hence here, 

 magnification one-fifth. Let us now see the utility 

 of this and how we can thus find the exact focal 

 length ot our lenses. It is not even necessary to 

 know the centre C ot the lens let us find the 

 exact position of the front focal point by taking 

 the lens out of the camera and holding the reverse 

 side to the sun and noting very carefully and 

 ex.-vctly the distance of the sun s imige trom the 

 front of the mount or hood of the lens we thus 

 know the front focal point F (Fig.t,). Then screw 

 the lens into the camera front and oarefullj focus 

 the sun on the ground glass, and thus find the back 

 focal paint F. Now rack out the camera an exact 

 and known distance, say, two or three inchen ; thi» 

 distance is y. Then place an object in front of the 



camera and move to and fro o""' «f'="y ' « f^o^t 

 then the distance of this object from the font 

 focal point is x. Now we know ./, ^ry therefore 

 V^i,-.that is to say, multiply tog^tl^" ^^'J 

 y and extract the square root, gives us the exact 

 focal length. 



